How to calculate "blend" based on "spot size" and inner cone angle?
From the Blender Wiki:


  The value is proportional and represents that amount of space that the
  inner cone should occupy inside the outer cone (SpotSi).


This is quite confusing, because the value is calculated by subtracting the area of the smaller circle from the area of the larger one instead.

R = bigest Radius
r = smallest Radius

blend = π(R*R - r*r) / π(R*R)


It should be:

blend = (R*R - r*r) / (R*R)


blend = 1 -&gt; r = 0
blend = 0 -&gt; r = R




BUT the result is not exactly what I expected.



In this example, the smaller black circle is half as large as the radius of the larger circle.

The orange lines are the cones of the spotlight obtained from the formula:

blend = (R*R - r*r) / (R*R) = 0.75


This is the manual setting (blend 0.71):